This invention relates to an electrodynamic system comprising a variable reluctance machine with a stator frame, several stator poles, a rotor, several rotor poles and a main winding supported by the stator poles, in combination with a rotor position transducer means and a semiconductor controlled uni-directional current source connected with its output side to the winding and with its input side to said means, the current varying between a maximum and a minimum value in time synchonism with the rate of change of the degree of overlapping between rotor and stator pole surfaces.
The reluctance machine referred to, whether a motor or generator, may be considered to belong to the so-called "stepping-motor" type, but whereas hitherto such machines have been only capable of use for purposes where relatively low power is required, for example, for step-wise operation of machine tools, by means of the electrodynamic system and improved construction of reluctance machine according to the invention continuous operation with improved torque and greatly improved efficiency may be obtained, there being extremely low inductive energy storage, with corresponding more complete conversion of instantaneous electrical input to mechanical output, or vice versa in the case of a generator, over a controllable range. Consequently the invention renders economically possible the use of a reluctance motor for such purposes as vehicle traction or for industry generally, the system enabling the operation of the motor to be readily controlled with less complicated and expensive circuitry arrangements than hitherto proposed for conventional electrical machines. A particularly high efficiency ratio, i.e. output/input, is also obtained when the machine is operated as a generator.
Magnetic saturation has heretofore been regarded as a factor limiting the performance of electrical machines. In the reluctance machine provided by the invention however, special steps are taken to ensure magnetic saturation, which is restricted to the interface areas where stator and rotor pole faces overlap, as a result of which the tangential force produced between the over-lapping pole faces may be almost doubled in comparison with known constructions.
In order to explain the basis of the invention and the means whereby the abovementioned objects are achieved reference is made in the following description to a number of diagrams which are shown in FIGS. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13, of the accompanying drawings, a full list of which is given below.
It is known that for single-excited non saturating poled devices a maximum of only one half of the electrical power input at constant current can be converted to mechanical form, the remainder being stored inductively. For the idealised saturated case it will be shown that the elimination of inductive energy storage leads to a doubling of the energy converted to mechanical form. The results are most meaningful to the invention when related to the pole overlap zone where the forces act. This zone may be considered to be "driven" by the magneto motive force F developed across the airgap for the magnetically linear case (FIG. 4), or across saturated ferro-magnetic material in the saturated case (FIG. 5). It will be shown that the tangential force between overlapping surfaces approaches ideal values:
f (newtons) = 0.5 FBL for the magnetically linear case (1)
f (newtons) = FBL for the saturated case (2)
B is the flux-density normal to the overlapped surfaces.
L is transverse length of the overlapped surfaces.
The equation (1) is well known, but equation (2) is new and unexpected.
FIG. 6 shows two of a family of curves describing the magnetization characteristic of a device as a function of a mechanical displacement x. The mechanical energy output at constant current is given by the increase in co-energy .DELTA.N.sub.fld ' shown by the curve-bounded hatched area x.sub.1, x.sub.2, 0, while the electrical energy input is given by the rectangular hatched area .psi..sub.1, .psi. .sub.2, x.sub.1, x.sub.2. The average force (or torque) is the curved hatched area divided by the mechanical displacement ##EQU1##
The overlap is assumed to be sufficient to make the end fringing effects dependent on the driving magneto motive forces F only, so that a displacement .DELTA.x at constant current merely extends the middle zone wherein the flux and stored energy spatial distributions are uniform. The magnetization characteristic of the overlap zone can be described by a B - F relation as in FIG. 8. Outside the overlap zone (dotted boundaries), the iron is assumed to be infinitely permeable.
For the displacement .DELTA.x, which introduces an extra flux .DELTA..phi. = BL.DELTA.x where L is the transverse length, ##EQU2## dividing through by L.DELTA. x and re-arranging ##EQU3## or, referring to FIG. 8 transverse force density ##EQU4##
Effectively, Equation 6 is a variant of the general statement of Equation 4 that mechanical force is given by the rate of change of co-energy with respect to mechanical displacement. it may be noted that the driving magneto motive force F is not restricted to one source but may be the resultant of a number of component magneto motive forces.
In the magnetically linear case the driving mmf is taken to be completely developed across an airgap such as that of FIG. 4. In the ideal saturated case, FIG. 5, the driving mmf is taken to be completely developed across saturated material having an infinitely narrow rectangular hysteresis loop.
Corresponding to FIG. 6, FIGS. 9 and 10 compare the characteristics of the two cases, the gap flux densities, dimensions, etc., being presumed the same.
The electrical energy input, as the flux linkage increases from .psi..sub.A to .psi..sub.B at constant current, is the same for the two cases, being the rectangular areas ABCD and A'B'C'D' = I .DELTA..psi..
For the magnetically linear case, the mechanical output is the triangular hatched area OAB = 0.5 I.DELTA..psi.. The increase in field stored energy is therefore, by difference, also equal to 0.5 I.DELTA..psi.. This is the well-known result for singly excited linear "reluctance-type" devices that, at constant current, a maximum of one half of the electrical input is convertible to mechanical form.
For the ideally saturated case, the mechanical output is the hatched area A'B'C'D' = I.DELTA..psi.. There is no inductively stored energy. The electrical input is completely converted to mechanical output.
Only a limited displacement has been considered above. In FIGS. 11 and 12 saturation curves corresponding to the positions for maximum and minimum flux are represented. Ideally, the minimum flux would be a negligible fraction of the maximum flux.
The total energy input, as the flux linkage increases from .psi..sub.min to .psi..sub.max at constant current, is I (.psi. .sub.max - .psi..sub.min) in both cases. The mechanical output energies correspond to the areas shown cross-hatched. If the minimum flux can be considered a negligible fraction of the maximum flux,
electrical input energy = I.phi..sub.max = F.phi..sub.max = (7) mechanical output energy for the ideal saturated case = I.phi..sub.max = F.phi..sub.max (8) mechanical output energy for the ideal linear case = 1/2 I.phi..sub.max = 1/2F.phi..sub.max (9) = 1/2 L.sub.max I.sup.2
Reverting now to the particular case of FIG. 7, the mechanical force equations 5 and 6 reduce to very simple form. For the magnetically linear case ##EQU5## EQU f/1 = 1/2 FB newtons/meter (10)
For ideally saturated case ##EQU6## EQU f/1 = FB newtons/meter (11)
In applying the aforementioned principles to obtain efficient energy conversion, it will be clear that the means should include for maximizing the cross-hatched area representing mechanical work shown in FIGS. 11 and 12.
FIG. 13 shows measured characteristics obtained from an experimental machine constructed according to the invention. The six upper magnetization curves correspond to different degrees of pole overlap. The lowest corresponds to a maximum reluctance position of the rotor.
The ratio of the area 0 - I - II - III - 0 representing energy converted and the area 0 - III - II - IV - 0 representing the maximum energy stored is approximately 9 : 1. It will be noted that the increments .DELTA..psi. are substantially position-dependent rather than current-dependent.
The cyclic process for electro-mechanical energy conversion (motor action) includes the four steps shown by arrows on FIG. 13 and begins when the rotor is in the maximum reluctance position. Step 0 - I shows the current increase to a working value when the flux increase is small. Step I - II shows the flux increase at constant current when the rotor-stator overlap increases from a minimum to a maximum. Step II - III shows the current being greatly reduced for small decrease in flux linkage. Step III - 0 shows the flux linkage being reduced to zero at substantially zero current, as the rotor poles move past the position of maximum overlap cross-section with the stator poles to reach a new position of maximum reluctance.